An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < 8 N , -6 N># and the second is #F_2 = < 2 N, 7 N>#. What is the object's rate and direction of acceleration?
The question gives two forces in vector form.
The first step is to find the net force acting upon the object. This can be calculated by vector addition.
The sum of two vectors
#< a,b >#and #< c,d >#is #< a+c,b+d>#.
Add the two force vectors
The next step is to find the magnitude of the vector, which is necessary to find the "size" of the force.
The magnitude of a vector
#< a,b >#is #sqrt(a^2+b^2)#.
The "size" of the force is
According to Newton's second law of motion, the net force acting upon an object is equal to the object's mass times its acceleration, or
Newton's first law of motion also states that the direction of acceleration is equal to the direction of its net force. The vector of its net force is
The angle "theta" of a vector
#< a,b >#is #tan(theta)=b/a#.